The Eurovision Song Contest is organized by the European Broadcasting Union (EBU) an organization set up to regulate TV tech. In short they exist to make sure a TV bought in Spain also works in Sweden. As such the EBU also grants full membership to countries that are not part of Europe but have strong economic ties with the continent and therefore are part of the European Broadcasting Area. That's how we got Israel in the contest. Australia also competes because (a) they are an associate member (b) they have an long history of airing the contest even before they competed (c) they spend a large sum of money every year to make the EBU forget where exactly Australia is located.

The US doesn't participate but a couple of years ago NBC bought the rights and tried to mount an "American Song Contest". It didn't work all that well because it was hamstrung by the rigid structure of American network TV. The ESC works (in part) because it is three nights only and they tried to make an entire season of television.